Barros monica isf2012

A Hybrid A Hybrid NeuroNeuro--Fuzzy System and Fuzzy System and Neural Network Approach to Neural Network Approach to

Forecast the Electricity Spot Price Forecast the Electricity Spot Price

[email protected]@mbarros.com 1

Forecast the Electricity Spot Price Forecast the Electricity Spot Price in Brazilin Brazil

Mônica Barros, Mônica Barros, D.Sc.D.Sc.Lucio de Medeiros, D.Sc.Lucio de Medeiros, D.Sc.

June, 2012June, 2012

AcknowledgmentAcknowledgment

� This work was sponsored by Norte Fluminense Thermal Plant (UTE Norte Fluminense) through a R&D grant.


ContentsContents

� Background

� Neural networks and Neuro-Fuzzy systems

� An Overview of the Data

� The Model - Hybrid neural network/neuro-fuzzy model for the spot price


fuzzy model for the spot price� Comments on the choice of the ANN Model

� Comments on the NFS set-up

� The structure of the hybrid model

� Empirical results

� Conclusions

BackgroundBackground

� The aim is to present a Hybrid Neuro-Fuzzy/Neural Network model which incorporates inflow information to forecast the weekly spot prices in the Southeast subsystem of Brazil.

� The Southeast subsystem corresponds to the most densely populated and industrialized


most densely populated and industrialized portion of Brazil.

� Part of the region is subject to occasional severe droughts that impact electricity generation.


� Power generation in Brazil is primarily hydroelectric, and hydro plants account for about 82% of the electricity generation in the country.

� Power plants are connected through long distances by a complex array of power lines, in what forms the so-called Brazilian interconnected system (SIN).


so-called Brazilian interconnected system (SIN).

� SIN comprises about 97% of the total energy produced in the country.

� The concept of subsystem is intrinsically related to the concept of “equivalent reservoir”.


� Spot prices in Brazil are computed through an optimization process that attempts to minimize costs in equivalent reservoirs, one for each of 4 subsystems.

� Electricity spot prices are calculated through a sequence of complex optimization models that produce the marginal cost of operation.


produce the marginal cost of operation.

� These models attempt to minimize the total cost of operations, computed as the sum of current and future costs.

� These costs are functions of (among other variables) the expected future inflows, the expected demand and the current reservoir levels.


� “ONS”, the Brazilian Independent System Operator (ISO) employs a model based on Stochastic Dual Dynamic Programming to perform operations planning.

� This model groups hydroelectric power plants of basins with similar hydrological behavior into the


basins with similar hydrological behavior into the so-called equivalent subsystems.

� Four equivalent subsystems (North, Northeast, Southeast/Central-West and South regions) are used.

� Hydrological scenarios are built into the system through a PAR(p) – Periodic Autoregressive Model.


� Two quantities play an important role to determine spot prices:

� “Stored energy” - maximum storage of the reservoir or basin;

� “Natural inflow energy” – river inflows, expressed in energy units.

Paranaíba and Grande river basins are the main


� Paranaíba and Grande river basins are the main basins in the Southeast subsystem, accounting for slightly over 60% of the subsystem’s reservoir’s capacity.

Neural networksNeural networks

� ANNs have been extensively used in time series forecasting, due to their generalization and learning abilities.

� They can identify nonlinear characteristics of complex series.

� The architecture of a Mutilayer Perceptron (MLP) network is:


network is:

NeuroNeuro--Fuzzy systemsFuzzy systems

� Neuro-fuzzy systems attempt to combine the advantages of both approaches: neural networks and fuzzy systems.

� We use the ANFIS neural fuzzy inference system proposed by Jang.


An Overview of the DataAn Overview of the Data

� The spot series consists of 471 weekly observations (May 2002 to May 2011)

500

600

Spot Price - Southeast Subsystem


0

100

200

300

400

05/1

1/0

2-0

5/1

7/0

2

09/2

8/0

2-1

0/0

4/0

2

02/1

5/0

3-0

2/2

1/0

3

07/0

5/0

3-0

7/1

1/0

3

11/2

2/0

3-1

1/2

8/0

3

04/1

0/0

4-0

4/1

6/0

4

08/2

8/0

4-0

9/0

3/0

4

01/1

5/0

5-0

1/2

1/0

5

06/0

4/0

5-0

6/1

0/0

5

10/2

2/0

5-1

0/2

8/0

5

03/1

1/0

6-0

3/1

7/0

6

07/2

9/0

6-0

8/0

4/0

6

12/1

6/0

6-1

2/2

2/0

6

05/0

5/0

7-0

5/1

1/0

7

09/2

2/0

7-0

9/2

8/0

7

02/0

9/0

8-0

2/1

5/0

8

06/2

8/0

8-0

7/0

4/0

8

11/1

5/0

8-1

1/2

1/0

8

04/0

4/0

9-0

4/1

0/0

9

08/2

2/0

9-0

8/2

8/0

9

12/0

9/1

0-0

1/1

5/1

0

05/2

9/1

0-0

6/0

4/1

0

10/1

6/1

0-1

0/2

2/1

1

03/0

5/1

1-0

3/1

1/1

1

Sp

ot p

ric

e (

R$

/MW

h)

week


� From the previous figure two striking features emerge:

� prices tend to stay at very low levels for long periods, but

� they also exhibit high volatility.

� Both features are common in primarily based hydroelectric systems, such as the Brazilian.


hydroelectric systems, such as the Brazilian.

� The high volatility of the series is also due to the non-storability of electricity and it is observed even in markets where prices are “actual” market prices, a consequence of bid and ask interactions, and not the result of optimization models, as in the Brazilian case.


� Log-returns based on the weekly prices

� Extreme weekly returns (in excess of ±50%) are not uncommon in the sample

75%

100%

125%

150%

Weekly log Return Statistics Spot Price (R$/MWh) Weekly Return (%)

Mean 54.33 -0.1%

Median 27.95 0.0%

Mode 18.59 0.0%


-200%

-175%

-150%

-125%

-100%

-75%

-50%

-25%

0%

25%

50%

05/1

1/0

2-0

5/1

7/0

2

08/3

1/0

2-0

9/0

6/0

2

12/2

1/0

2-1

2/2

7/0

2

04/1

2/0

3-0

4/1

8/0

3

08/0

2/0

3-0

8/0

8/0

3

11/2

2/0

3-1

1/2

8/0

3

03/1

3/0

4-0

3/1

9/0

4

07/0

3/0

4-0

7/0

9/0

4

10/2

3/0

4-1

0/2

9/0

4

02/1

2/0

5-0

2/1

8/0

5

06/0

4/0

5-0

6/1

0/0

5

09/2

4/0

5-0

9/3

0/0

5

01/1

4/0

6-0

1/2

0/0

6

05/0

6/0

6-0

5/1

2/0

6

08/2

6/0

6-0

9/0

1/0

6

12/1

6/0

6-1

2/2

2/0

6

04/0

7/0

7-0

4/1

3/0

7

07/2

8/0

7-0

8/0

3/0

7

11/1

7/0

7-1

1/2

3/0

7

03/0

8/0

8-0

3/1

4/0

8

06/2

8/0

8-0

7/0

4/0

8

10/1

8/0

8-1

0/2

4/0

8

02/0

7/0

9-0

2/1

3/0

9

05/3

0/0

9-0

6/0

5/0

9

09/1

9/0

9-0

9/2

5/0

9

12/0

9/1

0-0

1/1

5/1

0

05/0

1/1

0-0

5/0

7/1

0

08/2

1/1

0-0

8/2

7/1

0

12/1

1/1

0-1

2/1

7/1

0

04/0

2/1

1-0

4/0

8/1

1(%)

week

Mode 18.59 0.0%

Standard Deviation 66.54 30.6%

Kurtosis 23.89 7.63

Skewness 3.92 -0.44

Minimum 4.0 -194.2%

Maximum 569.59 138.8%

Count 471 470


� Natural Inflow Energy in the Southeast Subsystem presents a distinct seasonal pattern.

20000

25000

Na

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(A

ve

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Natural Inflow Energy - Paranaíba and Grande River Basins

Natural Inflow Energy (Paranaíba) Natural Inflow Energy (Grande)


0

5000

10000

15000

05/1

1/0

2-0

5/1

7/0

2

08/3

1/0

2-0

9/0

6/0

2

12/2

1/0

2-1

2/2

7/0

2

04/1

2/0

3-0

4/1

8/0

3

08/0

2/0

3-0

8/0

8/0

3

11/2

2/0

3-1

1/2

8/0

3

03/1

3/0

4-0

3/1

9/0

4

07/0

3/0

4-0

7/0

9/0

4

10/2

3/0

4-1

0/2

9/0

4

02/1

2/0

5-0

2/1

8/0

5

06/0

4/0

5-0

6/1

0/0

5

09/2

4/0

5-0

9/3

0/0

5

01/1

4/0

6-0

1/2

0/0

6

05/0

6/0

6-0

5/1

2/0

6

08/2

6/0

6-0

9/0

1/0

6

12/1

6/0

6-1

2/2

2/0

6

04/0

7/0

7-0

4/1

3/0

7

07/2

8/0

7-0

8/0

3/0

7

11/1

7/0

7-1

1/2

3/0

7

03/0

8/0

8-0

3/1

4/0

8

06/2

8/0

8-0

7/0

4/0

8

10/1

8/0

8-1

0/2

4/0

8

02/0

7/0

9-0

2/1

3/0

9

05/3

0/0

9-0

6/0

5/0

9

09/1

9/0

9-0

9/2

5/0

9

12/0

9/1

0-0

1/1

5/1

0

05/0

1/1

0-0

5/0

7/1

0

08/2

1/1

0-0

8/2

7/1

0

12/1

1/1

0-1

2/1

7/1

0

04/0

2/1

1-0

4/0

8/1

1

Na

tura

l In

flo

w E

ne

rgy

(A

ve

rag

e M

W)

week


� Spot prices and Natural Inflow Energy (ENA) exhibit an inverse relationship

140

160

180

100.000

120.000

Natu

ral In

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w E

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(A

ve

rag

e M

W)

Spot Price and Natural Inflow Energy - 2010 and 2011

Natural Inflow Energy (SE) Spot Price (R$/MWh)


0

20

40

60

80

100

120

140

0

20.000

40.000

60.000

80.000

01/0

2/1

0-0

1/0

8/1

0

01/1

6/1

0-0

1/2

2/1

0

01/3

0/1

0-0

2/0

5/1

0

02/1

3/1

0-0

2/1

9/1

0

02/2

7/1

0-0

3/0

5/1

0

03/1

3/1

0-0

3/1

9/1

0

03/2

7/1

0-0

4/0

2/1

0

04/1

0/1

0-0

4/1

6/1

0

04/2

4/1

0-0

4/3

0/1

0

05/0

8/1

0-0

5/1

4/1

0

05/2

2/1

0-0

5/2

8/1

0

06/0

5/1

0-0

6/1

1/1

0

06/1

9/1

0-0

6/2

5/1

0

07/0

3/1

0-0

7/0

9/1

0

07/1

7/1

0-0

7/2

3/1

0

07/3

1/1

0-0

8/0

6/1

0

08/1

4/1

0-0

8/2

0/1

0

08/2

8/1

0-0

9/0

3/1

0

09/1

1/1

0-0

9/1

7/1

0

09/2

5/1

0-1

0/0

1/1

0

10/0

9/1

0-1

0/1

5/1

0

10/2

3/1

0-1

0/2

9/1

0

11/0

6/1

0-1

1/1

2/1

0

11/2

0/1

0-1

1/2

6/1

0

12/0

4/1

0-1

2/1

0/1

0

12/1

8/1

0-1

2/2

4/1

0

01/0

1/1

1-0

1/0

7/1

1

01/1

5/1

1-0

1/2

1/1

1

01/2

9/1

1-0

2/0

4/1

1

02/1

2/1

1-0

2/1

8/1

1

02/2

6/1

1-0

3/0

4/1

1

03/1

2/1

1-0

3/1

8/1

1

03/2

6/1

1-0

4/0

1/1

1

04/0

9/1

1-0

4/1

5/1

1

04/2

3/1

1-0

4/2

9/1

1

05/0

7/1

1-0

5/1

3/1

1

Sp

ot p

ric

e (

R$/M

Wh

)

Natu

ral In

flo

w E

ne

rgy

(A

ve

rag

e M

W)

week

The ModelThe Model

� Hybrid neural network/neuro-fuzzy model for the spot price� Comments on the choice of the ANN Model

� Comments on the NFS set-up

� The structure of the hybrid model


The ModelThe Model

� The proposed model is a combination of a backpropagation ANN and an ANFIS-type NFS.

� In our model, the ANN forecasts are added to the original inputs and fed to NFS to generate the spot price forecasts.


� Suppose the original ANN model contains n inputs. The final “hybrid” model will contain (n+1) inputs, the original ones plus an additional input, obtained by “fitting” the ANN to the dataset, generating one-step ahead forecasts and adding the one-step ahead forecasts as an additional input variable.

The ModelThe Model

� We created six different hybrid models.

� Each model specializes in a single forecasting horizon (one to 6 weeks ahead).

� Comments on the Choice of the ANN Model:� Comments on the Choice of the ANN Model:

� The network structures for each model class include an intermediate layer with a sigmoidal activation function and an output layer with a linear activation function.

� ANNs with 6, 7, 8, 9, 10, 11 and 12 neurons in the intermediate layer were tested.


The ModelThe Model

� Comments on the Choice of the ANN Model:

� For each of these numbers of neurons, we tested networks with 1000 to 3000 epochs.

� The training period used for choosing the ANN models was 90% of the data set.


� One of the major issues regarding ANNs is the dependence on the initial weights.

� Due to this fact, the results produced by networks with the same structure may vary considerably.

The ModelThe Model

� Comments on the Choice of the ANN Model:

� In search of a more robust procedure, we replicate the same network architecture several times and chose the particular network that led to the smallest one-step ahead MAPE in the training period.

We tested 21, 25, 31, 51, 75, 101, 121, 131, 151


� We tested 21, 25, 31, 51, 75, 101, 121, 131, 151 replications of the same structure of several different ANN models.

� We chose to use 75 replications of each architecture. In each, the ANN which produces the best result (lowest MAPE).

The ModelThe Model

� Comments on the NFS Set-up:

� As with the ANN model, several choices have to be made regarding the specification of the NFS implementation.

� The neuro-fuzzy system with n inputs most often outperformed the ANN with the same inputs.


� The hybrid model consists of two steps:� 1) Choose the “best” ANN with n inputs and record its one

step ahead forecasts;

� 2) Fit a NFS with the previous n inputs and an additional one, the one step ahead forecasts obtain in the previous step.

� The entire system requires a very modest amount of information – just the past prices and past natural inflow energy time series, which should be updated weekly.

The ModelThe Model

� The structure of the Hybrid Model:

� the hybrid forecasting approach is a two step procedure:

� in the first step, 75 replications of a MLP neural network with these inputs are adjusted and the best network is selected, using as a criterion the minimum MAPE during the training period


minimum MAPE during the training period

� The second step employs the previously mentioned inputs AND the forecasts generated by the best ANN obtained in the first step as inputs in an ANFIS neuro-fuzzy system

� the objective of this model is to generate forecasts up to six weeks in advance.

The ModelThe Model� The structure of the Hybrid Model:

� Let P(t) denote the price at week t, and suppose it denotes the current week.

� The forecast for P(t+1) uses as inputs the current and lagged values of the spot prices and the natural inflow energies at the subsystem and the basins,


inflow energies at the subsystem and the basins, namely:

� P(t), P(t-2),

� ENA_SE(t) (inflow energy of the subsystem at the current week),

� ENA_SE(t-1) (inflow energy of the subsystem one week ago),

� ENA_GR(t-1) (inflow energy of the Grande river basin one week ago),

� ENA_PA(t) (inflow energy of the Paranaíba river basin at the current week) .

The ModelThe Model

� The structure of the Hybrid Model:

� It is necessary to forecast the input variables.

� The forecasts of all natural inflow energy series (ENA_SE, ENA_GR and ENA_PA) are obtained exogenously through univariate time series models, chosen to minimize the Bayesian Information Criterion (BIC).


Criterion (BIC).

Natural inflow energy series

Model Structure R2 adjusted MAPEDurbin-Watson

Southeast SARIMA(1,0,2)x(2,0,1) on ln of actual data 90.8% 12.1% 1.94

Paranaíba SARIMA(1,0,0)x(1,0,0) on ln of actual data 87.7% 17.4% 1.99

Grande SARIMA(1,0,2)x(2,0,1) on ln of actual data 85.6% 18.7% 1.92

Empirical ResultsEmpirical Results

� Southeast spot price six-step ahead forecasts at the week Jan 1–7, 2011

52.2

50

60

Spot price six-steps ahead forecasting at week Jan 1-7, 2011

FORECAST ACTUAL


14.4

30.5

23.9

12.1

27.5

30.2

18.6

26.1

22.6

12.1

39.9

0

10

20

30

40

Jan 8-14, 2011 Jan 15-21, 2011 Jan 22-28, 2011 Jan 29-Feb 4, 2011 Feb 5-11, 2011 Feb 12-18, 2011

Sp

ot p

ric

e (

PL

D) in

R$

/MW

h

week


� Southeast spot price six-step ahead forecasts at the week Feb 26–Mar 04, 2011

36,6135,92

35

40

Six-steps ahead forecasting

at week Feb 26-Mar 04, 2011


12,08 12,08

17,00

12,08 12,0812,0813,47

12,08 12,08 12,08

0

5

10

15

20

25

30

Mar 05-11, 2011 Mar 12-18, 2011 Mar 19-25, 2011 Mar 26-Apr 01, 2011 Apr 02-08, 2011 Apr, 09-15, 2011

Sp

ot

pri

ce (

PLD

) in

R$

/MW

h

FORECAST ACTUAL


� Error statistics of the six step ahead forecasts (%)

Forecasts starting at week:1 step

ahead

2 steps

ahead

3 steps

ahead

4 steps

ahead

5 steps

ahead

6 steps

ahead

MAPE

(week)

Jan 1-7, 2011 22.67 17.22 5.59 0.00 31.01 42.21 19.78

Jan 8-14, 2011 55.86 4.96 46.57 94.26 34.56 47.90 47.35

Jan 15-21, 2011 1.76 46.57 32.12 53.27 60.67 55.16 41.59

Jan 22-28, 2011 46.57 32.12 53.08 60.54 55.03 85.66 55.50


Jan 29-Feb 4, 2011 32.12 53.08 60.54 55.03 85.66 212.91 83.22

Feb 5-11, 2011 7.70 20.10 29.11 85.66 192.26 65.35 66.70

Feb 12-18, 2011 5.43 15.38 85.66 193.21 64.91 24.02 64.77

Feb 19-25, 2011 26.09 0.00 1.91 6.52 38.35 0.00 12.15

Feb 26-Mar 04, 2011 0.00 1.91 10.32 40.71 0.00 0.00 8.82

MAPE (forecast horizon) 22,02 21,26 36,10 65,47 62,49 59,25


� Forecasts produced in week April 9th-15th, 2011 and the following ones tend to be higher than the actual values, and sometimes the forecast errors are quite high, for no apparent reason

26,16

34,00

39,7938,69 38,16

43,40

35,92

60000

80000

100000

120000

25

30

35

40

45

50

So

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Actual values, Six-steps ahead forecasts

at week Apr 9-15, 2011 and Inflow Energy time series

FORECAST ACTUAL Southeast Inflow Energy


apparent reason

� a possible explanation for this fact is that the subsystem inflow energy has a decreasing trend on the weeks preceding April 9th-15th, 2011.

12,0813,47

12,08 12,08 12,08 12,08 12,08

15,6213,91

15,6417,09

0

20000

40000

60000

0

5

10

15

20

25

March 5 -

11, 2011

March 12

-18, 2011

March 19

-25, 2011

March 26

-Apr 1,

2011

Apr 2-8,

2011

Apr 9-15,

2011

Apr 16-22,

2011

Apr 23-29,

2011

Apr 30-

May 6,

2011

May 7-13,

2011

May 14-

20, 2011

May 21-

27, 2011

So

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En

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� This behavior, in a hydro based system, would lead to the dispatch of thermal plants to save water and increase reservoir levels resulting in an increase in the spot price.

ConclusionsConclusions

� The input variables considered are thought of as important leading indicators of price movements in a primarily hydroelectric system such as Brazil’s

� The forecasts produced were adequate most of the time. However, in some instances, short-term dispatch decisions affected prices in ways


term dispatch decisions affected prices in ways that could not be anticipated by the model

ConclusionsConclusions

� The model can be improved further by incorporating other variables, specifically those related to thermal generation.

� In fact, a trial neuro-fuzzy model has been tested to forecast thermal generation, and the forecast can be used as a “threshold” – if above a certain amount, the forecast of the


above a certain amount, the forecast of the original model need to be corrected upwards to account for the dispatch of the thermal plants. These results are, however, at a very preliminary stage, so they were not reported here.

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